Deriving Coulomb's law and other fundamental equations from F=ma?

[Queequeg]

I saw a joke crib sheet for a physics class that said "F=ma, derive the rest," but is it actually possible to derive at least electricity and magnetism questions from Newton's second law?

 

[TrueBrit]

No, you can't derive electricity and magnetism from Newton't equations. For example, there is no way the charge on an electron could be derived, nor could the fact that like charges repel and unlike charges attract, and nor could the fact that a varying magnetic field induces a current in a wire.

 

[MrRobotoToo]

I saw a joke crib sheet for a physics class that said "F=ma, derive the rest," but is it actually possible to derive at least electricity and magnetism questions from Newton's second law?

Not from Newton's law. But both the scalar and vector potentials are required if one demands the covariance of, say, Schrödinger's equation under local phase transformations of the wavefunction. Electromagnetism is ultimately explainable by a fundamentally quantum mechanical symmetry.

 

[TheDemx27]

Perhaps they were just talking about deriving most of classical mechanics.